Martingale transforms goodness-of-fit tests in regression models

被引:82
作者
Khmaladze, EV
Koul, HL
机构
[1] Victoria Univ Wellington, Sch Math & Comp Sci, Wellington, New Zealand
[2] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA
关键词
asymptotically distribution free; partial sum processes;
D O I
10.1214/009053604000000274
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
This paper discusses two goodness-of-fit testing problems. The first problem pertains to fitting an error distribution to an assumed nonlinear parametric regression model, while the second pertains to fitting a parametric regression model when the error distribution is unknown. For the first problem the paper contains tests based on a certain martingale type transform of residual empirical processes. The advantage of this transform is that the corresponding tests are asymptotically distribution free. For the second problem the proposed asymptotically distribution free tests are based on innovation martingale transforms. A Monte Carlo study shows that the simulated level of the proposed tests is close to the asymptotic level for moderate sample sizes.
引用
收藏
页码:995 / 1034
页数:40
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